Source labels openChecked July 26, 2026

Erdős Problem 887: Rosenfeld 4

Erdős and Rosenfeld, ask whether $4$ is the best possible $K$ for the infinitude of $n$ with (at least) $K$ divisors in $(n^{\frac{1}{2}}, n^{\frac{1}{2}} + n^{\frac{1}{4}})$ .

Number theory AMS 11

Mathematical statement

Erdős and Rosenfeld, ask whether $4$ is the best possible $K$ for the infinitude of $n$ with (at least) $K$ divisors in $(n^{\frac{1}{2}}, n^{\frac{1}{2}} + n^{\frac{1}{4}})$ .

Statement source: Erdős Problems statement material

Statement terms: Source-specific

Source-specific terms. Therefore does not assert reuse rights beyond attributed display.

Statement artifacts, not proofs

These records expose exact Lean propositions and statement-only wrappers. Defining a proposition does not supply a proof of it. A placeholder-bearing target also contains no proof. Elaboration checks syntax and types; it does not certify that a formalization perfectly captures every nuance of the informal problem.

Pinned Lean formulation 1

erdos_887.variants.rosenfeld_4

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem erdos_887.variants.rosenfeld_4 :    IsGreatest {K | ∃ C > (0 : ℝ),      Infinite {n : ℕ | K ≤ #{ d ∈ Ioo ⌊√n⌋₊ ⌈√n + C * n^((1 : ℝ) / 4)⌉₊ | d ∣ n }}} 4 := by  sorry

Statement source: Formal Conjectures
Lean version: v4.27.0
Placeholder: Present; no proof artifact
Source evidence: Pinned source index
Fidelity review: Community formulation

References

Pinned Formal Conjectures sourceformalization erdosproblems.com/887background